Exploring Magnetohydrodynamic Nanofluid Flow: A Fractional Differential Approach with Homotopy Perturbation Method

Introduction This paper investigates the heat and mass transfer processes in a steady nanofluid flow confined between two parallel plates under the influence of a uniform magnetic field. The model incorporates the effects of thermophoresis and Brownian motion, key phenomena in nanofluid dynamics, to better understand the fluid behavior. Objectives To enhance the model's accuracy and flexibility by reformulating the governing equations into fractional differential equations, which account for memory effects and non-local interactions in the flow dynamics. Methods The fractional model is analyzed using the Homotopy Perturbation Method (HPM), an effective semi-analytical technique that provides accurate solutions for nonlinear fractional differential equations. Conclusion The results reveal that the Nusselt number decreases with higher thermophoretic and Brownian parameters but increases with the viscosity coefficient. Additionally, nanofluid concentration decreases with increased Brownian motion but rises with the augmentation of the thermophoretic parameter. These findings underscore the advantages of the fractional approach in capturing complex dynamics in nanofluid flows.